HS AP Calculus

Announcement for Prospective Students: The first unit on limits will be shortened by two weeks in the Spring 2020 offering of the course. This will allow for 3 full weeks where we do not learn any new material. Instead, we will solely focus on practicing for the exam.

AP Calculus AB Exam Date: May 14, 2019 8 am

Test Format:
Section I: Multiple Choice | 45 Questions | 105 minutes | 50% of Exam Score
• Part A: 28 questions; 55 minutes (no calculator permitted)
• Part B: 17 questions; 50 minutes (graphing calculator permitted)
Section II: Free (Constructed) Response | 6 Questions | 90 minutes | 50% of Exam Score
• Part A: 2 problems; 30 minutes (graphing calculator permitted)
• Part B: 4 problems; 1 hour (no calculator permitted)


Syllabus


Week 1 (Unit 1: Limits)
What is Calculus?
2.1 Average Rates of Change
2.1 Numerical Limit
2.2 Definition of a Limit
2.2 One Sided Limits vs. Two Sided Limits
2.3 Limit Rules
2.3 Limits Laws

Week 2 (Unit 1: Limits)
2.2 Graphical Limits
Review of Polynomial Division
2.3 Limits of Polynomials and Rational Functions pg. 97
Techniques of Finding Limits
  • Direct Substitution
  • Cancellation (Factoring)
  • Radical Conjugate
  • Algebraic Manipulation
  • Making use of the formal definition of an absolute values
Special Limit: lim as x-> 0 sin(x)/x = 1

Week 3 (Unit 1: Limits)
2.2 Infinite Limits (Sign Analysis/Limit Analysis)
2.6 Limits at Infinity
Special Limit: lim as x->inf 1/x = 0
2.6 Horizontal Asymptotes
2.2 Asymptotes

Week 4 (Unit 1: Limits)
SNOW DAY
Review of Exponentials and Logarithms
Piece-wise Functions
2.3 Squeeze Theorem pg. 101

Week 5 (Unit 1: Limits)
Review of Domain and Range
2.5 Continuity
2.5 Combinations of Continuous Functions pg. 117
2.5 Library of Continuous Functions pg. 120 Theorem 7
2.5 Intermediate Value Theorem pg. 122

Exam 1 on Monday February 11, 2019 (Practice Exam)

Week 6 (Unit 2: Derivatives)
2.7 Derivatives by Definition
2.8 Equations of Tangent Lines
3.1 Derivative Rules

Week 7 (Unit 2: Derivatives)
3.2 The Product Rule
3.2 The Quotient Rule

Week 8 (Unit 2: Derivatives)
Special Derivative: The derivative of ln(x) is 1/x
3.3 Trigonometric Derivatives
3.4 The Chain Rule
3.5 Implicit Differentiation
3.6 Derivatives of Logarithms & Logarithmic Differentiation as a technique

Week 9 (Unit 2: Derivatives)
Inverse Trigonometric Derivatives
Equations of Normal Lines
Related Rates (NOT ON EXAM 2)

Unit 2 Exam Thursday March 7, 2019

Week 10 (Unit 3: Derivatives Applications)
Related Rates
Extreme Value Theorem
Critical Numbers

Week 11 (Unit 3: Derivatives Applications)
Extreme Values: Global (Absolute) vs. Local (Relative)
4.2 Mean Value Theorem
4.3 First Derivative Test for Local Extrema
Finding Absolute Extrema

Week 12 (Unit 3: Derivatives Applications)
4.3 Second Derivative Test
4.3 Concavity
4.3 Inflection Points
4.3 Find Local Extrema
4.3 & 4.5 Curve Sketching
4.4 L'Hopitals Rule & Indeterminant Forms
4.7 Optimization

Week 13 (Unit 4: Anti-Differentiation & Integrals)
Unit 3 Exam
4.8 Anti-Derivatives
Anti-Derivative S-V-A Word Problems

Week 14 (Unit 4: Integrals)
Unit 2 Test Re-Take and Review
5.1 Upper, Lower, Midpoint (7.7), Left-Hand, and Right-Hand Sums (Riemann Sums)
Integral Notation
5.2 Integrals as Area
5.2 Definite Integrals
5.2 Properties of Integrable Functions pg. 385-387
5.3 Fundamental Theorem of Calculus (Part II)
5.4 Indefinite Integrals and Net Change Theorem Distinguish between Total (Unsigned) Area and Net (Signed) Area. (Remember, integral notation refers to signed/net area)
6.5 Average Value of a Function

Week 15 (Unit 4: Integrals & Unit 5 Integral Applications)
5.3 Fundamental Theorem of Calculus (Part I) [And methods for adjusting limits of integration so that FTC I applies)
5.5 Substitution (Also called u-substitution)
7.7 Trapezoidal Sums (The last sum approximation that we will learn. Ignore everything else in this chapter that is not the midpoint or trapezoidal rule)
9.3 Separation of Variables (Only worry about the technique for the class example in this chapter)
Review: Calculator Use for:

Week 16 (Unit 5 Integral Applications & Course Review)
Monday Unit 4 Exam April 29, 2019
6.1 Area Between Curves
6.2 Volumes of Solids and Cross Sections
Wednesday Unit 5 Exam May 1, 2019
9.2 Review: Slope Fields
Review: Limits of Composite Functions
Review: Special Cases where Derivatives fail to exist (pg. 158)


Week 17 (Course Review & Full Practice Exams)

Week 18 (Exam Week)
A.P. Calculus AB Exam May 14, 2019 8 am